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 A263140 Expansion of Product_{k>=1} (1 + x^(2*k-1))^k. 11
 1, 1, 0, 2, 2, 3, 4, 5, 10, 11, 16, 20, 31, 39, 50, 71, 93, 124, 154, 211, 271, 357, 449, 587, 762, 968, 1233, 1571, 2021, 2535, 3220, 4049, 5145, 6431, 8070, 10105, 12670, 15784, 19619, 24447, 30348, 37635, 46464, 57532, 70945, 87477, 107456, 132192, 162220 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015 FORMULA G.f.: exp(Sum_{j>=1} (-1)^(j+1)/j*x^j/(1 - x^(2*j))^2). a(n) ~ exp(-Pi^4 / (5184*Zeta(3)) + Pi^2 * n^(1/3) / (8 * 3^(4/3) * Zeta(3)^(1/3)) + 3^(4/3) * Zeta(3)^(1/3) * n^(2/3)/4) * Zeta(3)^(1/6) / (2^(23/24) * 3^(1/3)* sqrt(Pi) * n^(2/3)). MATHEMATICA nmax = 100; CoefficientList[Series[Product[(1 + x^(2*k-1))^k, {k, 1, nmax}], {x, 0, nmax}], x] nmax = 100; CoefficientList[Series[E^Sum[(-1)^(j+1)/j*x^j/(1 - x^(2*j))^2, {j, 1, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A035528, A263149, A263150, A263199, A262878, A263138, A263145, A292037. Sequence in context: A184259 A014535 A210642 * A205006 A123560 A060407 Adjacent sequences: A263137 A263138 A263139 * A263141 A263142 A263143 KEYWORD nonn AUTHOR Vaclav Kotesovec, Oct 10 2015 STATUS approved

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Last modified February 8 14:10 EST 2023. Contains 360146 sequences. (Running on oeis4.)